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* And it is never mentioned which quaternions {{math|'''z'''<sub>l</sub>}} and {{math|'''z'''<sub>r</sub>}} must be used to achieve a desired rotation in 4-space, or what rotation is achieved using those '''z''''s.
[[Special:Contributions/50.205.142.35|50.205.142.35]] ([[User talk:50.205.142.35|talk]]) 20:45, 13 January 2020 (UTC)
:: Yes, there are some issues here. In addition, the equation
::<math>f(\vec{v})=\mathbf{z}_{\rm{l}} \vec{v} \mathbf{z}_{\rm{r}}=
\begin{pmatrix}
a_{\rm{l}}&-b_{\rm{l}}&-c_{\rm{l}}&-d_{\rm{l}}\\
b_{\rm{l}}&a_{\rm{l}}&-d_{\rm{l}}&c_{\rm{l}}\\
c_{\rm{l}}&d_{\rm{l}}&a_{\rm{l}}&-b_{\rm{l}}\\
d_{\rm{l}}&-c_{\rm{l}}&b_{\rm{l}}&a_{\rm{l}}
\end{pmatrix}\begin{pmatrix}
w\\x\\y\\z
\end{pmatrix}\begin{pmatrix}
a_{\rm{r}}&-b_{\rm{r}}&-c_{\rm{r}}&-d_{\rm{r}}\\
b_{\rm{r}}&a_{\rm{r}}&d_{\rm{r}}&-c_{\rm{r}}\\
c_{\rm{r}}&-d_{\rm{r}}&a_{\rm{r}}&b_{\rm{r}}\\
d_{\rm{r}}&c_{\rm{r}}&-b_{\rm{r}}&a_{\rm{r}}
\end{pmatrix}.
</math>
:: cannot be correct without the addition of a transposition or re-ordering. [[User:Lucaswilkins|Lucaswilkins]] ([[User talk:Lucaswilkins|talk]]) 23:59, 23 May 2021 (UTC)
== Compared to rotation matrices ==
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